The traditional tools of mechanical drawing include a T square and two special triangles. One of the triangles has angles measuring 30, 60, 90. The other has angles measuring 45, 45, and 90. The properties of these triangles make them especially useful in geometry as well as drawing.
-If you draw a diagonol of a square, two congruent isosceles triangles are formed.
Because the diagonals is the hypotenuse of a right triangle, its length can be found
by using the Pythagorean Theorem. Areas of Regular Polygons
To find the area of a regular hexagon, divide the hexagon into 6 congruent, non-overlapping equilibrium
triangles. Find the area of one triangle and multiply by 6 to find the area of a hexagon. Note that
the altitude of the equilerateral triangle is the longer leg of a 30-60-90 triangle. The altitude is 1/2 of the
length of the side of the hexagon multiplied by square root of 3.
Because the hexagon is composed of 6 congruent triangles, the area of the hexagon is found as follows: A=(100square root of 3)=600square root of 3 is aproximately 1039 square centimeters.
In any 45-45-90 triangle the length of the hypotenuse is 2 square root times the length of a leg.
30-60-90 Triangle Theorem:
In any 30-60-90 triangle, the length of the hypotenuse is 2 square root times the lengh of a leg.
30-60-90 triangle
45-45-90 triangle
The area, A, of a regular polygon with apothem a and perimeter p is given by: 1/2 (a*p).
Apothem: The altitude of a triangle from the center of the polygon to a side of the polygon
In a triangle, there is a relationship between the position of the longest and shortest sides of a triangle and the positions of its angles.
-If you draw a diagonol of a square, two congruent isosceles triangles are formed.
Because the diagonals is the hypotenuse of a right triangle, its length can be found
by using the Pythagorean Theorem.
Areas of Regular Polygons
To find the area of a regular hexagon, divide the hexagon into 6 congruent, non-overlapping equilibrium
triangles. Find the area of one triangle and multiply by 6 to find the area of a hexagon. Note that
the altitude of the equilerateral triangle is the longer leg of a 30-60-90 triangle. The altitude is 1/2 of the
length of the side of the hexagon multiplied by square root of 3.
Because the hexagon is composed of 6 congruent triangles, the area of the hexagon is found as follows: A=(100square root of 3)=600square root of 3 is aproximately 1039 square centimeters.
In any 45-45-90 triangle the length of the hypotenuse is 2 square root times the length of a leg.
30-60-90 Triangle Theorem:
In any 30-60-90 triangle, the length of the hypotenuse is 2 square root times the lengh of a leg.
30-60-90 triangle
45-45-90 triangle
The area, A, of a regular polygon with apothem a and perimeter p is given by: 1/2 (a*p).
Apothem: The altitude of a triangle from the center of the polygon to a side of the polygon
In a triangle, there is a relationship between the position of the longest and shortest sides of a triangle and the positions of its angles.